Perturbed Kitaev model: excitation spectrum and long-ranged spin correlations

Abstract

We developed general approach to the calculation of power-law infrared asymptotics of spin-spin correlation functions in the Kitaev honeycomb model with different types of perturbations. We have shown that in order to find these correlation functions, one can perform averaging of some bilinear forms composed out of free Majorana fermions, and we presented the method for explicit calculation of these fermionic densities. We demonstrated how to derive an effective Hamiltonian for the Majorana fermions, including the effects of perturbations. For specific application of the general theory, we have studied the effect of the Dzyaloshinskii-Moriya anisotropic spin-spin interaction; we demonstrated that it leads, already in the second order over its relative magnitude $D/K$, to a power-law spin correlation functions, and calculated dynamical spin structure factor of the system. We have shown that an external magnetic field $h$ in presence of the DM interaction, opens a gap in the excitation spectrum of magnitude $\Delta \propto Dh$.

12 pages, 3 figures

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Cited by in corpus (7)

• Impact of off-diagonal exchange interactions on the Kitaev spin liquid state of $\alpha$-RuCl${}_3$
• Novel chiral quantum spin liquids in Kitaev magnets
• Non-local spin correlation as a signature of Ising anyons trapped in vacancies of the Kitaev spin liquid
• Gauge Field Dynamics in Multilayer Kitaev Spin Liquids
• Deciphering competing interactions of Kitaev-Heisenberg-$\Gamma$ system in clusters: part I -- static properties
• Deciphering competing interactions of Kitaev-Heisenberg-$\Gamma$ system in clusters: part II -- dynamics of Majorana fermions
• A primer on Kitaev Model: Basic aspects, material realization, and recent experiments